A141838 - OEIS

%I #9 Jul 21 2017 17:29:46

%S 14,24,44,134,1014,13024,404044,100412134,201201142014

%N a(n) = first term that can be reduced in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n), such that b is always 4 so that each interpretation is base 5. Terms already fully reduced (i.e., single digits) are excluded.

%C It is possible to compute additional terms by taking the last term, treating it as base-10 and converting to base-5. This will necessarily create a term which can converted back to base 10 yielding the previous term in the sequence which will itself yield N further terms. But there is no guarantee (except in base 2) that the term so derived will be the first term to produce a sequence of N+1 terms. There could be another, smaller, term which satisfies that requirement but which uses different terms. Pushing the last term of this sequence yields 201201142014 as a possible next term.

%e a(3) = 44 because 44 is the first number that can produce a sequence of three terms by repeated interpretation as a base 5 number: [44] (base-5) --> [24] (base-5) --> [14] (base-5) --> [9]. Since 9 cannot be interpreted as a base 5 number, the sequence terminates with 14. a(1) = 14 because 14 is the first number that can be reduced once, yielding no further terms interpretable as base 5.

%Y Cf. A091049, A141836, A141837, A141839, A141840, A141841, A141842.

%K base,more,nonn

%O 1,1

%A Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008

%E a(9) from _Giovanni Resta_, Feb 23 2013